Markets Decide

Price Elasticity of Demand

Price elasticity of demand is how much quantity demanded moves when the price moves.

The questionIf we change the price, how much volume do we gain or lose, and does the trade pay?

Formula · Alfred Marshall, 1890

Below 1 in absolute value Inelastic A price rise raises revenue

Equal to 1 Unit elastic A price rise leaves revenue unchanged

Above 1 in absolute value Elastic A price rise lowers revenue

Schematic of how the absolute value of elasticity sets what a price rise does to revenue.

When to use it

A client plans a price increase or a promotion, and the argument is between "volume will collapse" and "they will pay."
A category manager must choose which items in a range can carry an increase and which have to be held.
A volume forecast after a price change has to be supported with evidence, not asserted.
A competitor has moved its prices, and the client needs a read on how much volume is exposed.

When to avoid it

The history has no usable price variation. Prices never moved, or every move came with a promotion or a product change. A controlled price test across matched stores or customer groups will teach more than the history.
The proposed change is much larger than anything seen before. An estimate near today's price will not hold far from it.
The result depends on a competitor's response, for example a rival that will match a cut within a week. The measured number assumes rivals stand still.
Price is negotiated deal by deal under contract or tender. There is no market-wide price and quantity relationship to estimate.

Overview

Price elasticity of demand measures how far the quantity customers buy moves when price moves. It is the percentage change in quantity divided by the percentage change in price. An absolute value above 1 means demand is elastic, so a price increase lowers revenue. Below 1 means inelastic, so an increase raises revenue. The measure supports pricing decisions and volume forecasts after a price change.

The number belongs to a specific item, price range, time horizon, and set of competitor prices. Estimates drawn from history are often contaminated by promotions and seasonality, and one figure for a whole portfolio hides items that behave very differently. Revenue is also not profit. Whether a price move pays depends on unit cost as well as elasticity.

How to read the number

Elastic (absolute value above 1)

Quantity moves by a larger percentage than price. A price increase lowers revenue, and a price cut raises it. Typical where close substitutes exist and the purchase is easy to postpone.

Inelastic (absolute value below 1)

Quantity moves by a smaller percentage than price. A price increase raises revenue, and a cut lowers it. Typical of items with few substitutes, a small share of the buyer's budget, or a switching cost.

Unit elastic (absolute value of 1)

The percentage changes match. Revenue stays the same when price changes, though cost and profit will not.

What moves the number

The availability and closeness of substitutes, the size of the purchase against the buyer's budget, how necessary the item is, and how much time buyers have to adjust. Elasticity is usually larger over a long period than a short one, because buyers have time to switch.

What it is not

A fixed property of a product. The number changes with the price range, the time period, competitors' prices, and the season.
A profit calculation. Elasticity says how revenue responds. Whether a change pays depends on unit cost too, and the example below shows a price increase that lowers revenue and still raises profit.
A measure of what any one customer will pay. It describes the combined response of a market at a particular price.

The steps

Set the decision and the range

Name the items, the customers, and the size of change under discussion, for example up to ten percent. An elasticity measured near the current price applies near the current price.
Assemble clean price and quantity history

Use the same product and market, with periods before and after a price change. Remove or flag promotions, stockouts, seasonality, competitor moves, and product changes. If you cannot, say how much of the movement is unexplained.
Calculate by item or segment

Apply the midpoint formula to each item or segment, not only to the portfolio. Show the spread across items. If you estimate with a regression instead, report the interval.
Translate to revenue and profit

Apply the elasticity to the proposed price to get a volume, then compute revenue, then profit using unit cost. Include any effect on sales of related items.
Stress-test and test in the market

Re-run the numbers with a competitor matching, and with a longer time horizon where volume loss is larger. Where the stakes justify it, run a controlled price test before rolling out.

The formula

Price elasticity of demand (E) = % change in quantity demanded ÷ % change in price, each change measured against the midpoint of the old and new values

For a 1 percent change in price, quantity demanded changes by about E percent in the opposite direction. The sign is negative for ordinary goods, so consultants usually quote the absolute value.

Q1 and Q2 are quantity demanded before and after the price change, for the same product, market, and period length.
P1 and P2 are the price before and after.
Midpoint method: % change in quantity = (Q2 - Q1) ÷ ((Q1 + Q2) ÷ 2), and % change in price = (P2 - P1) ÷ ((P1 + P2) ÷ 2). Using the average as the base gives the same answer for a rise and a fall between the same two points.
Revenue test: if the absolute value of E is above 1, a price increase lowers revenue. If it is below 1, a price increase raises it. At 1, revenue does not change.
Profit test: compare (price minus unit cost) × quantity before and after. The revenue test alone does not decide it.

In practice

A foodservice distributor raised list prices on two items by about the same percentage and kept weekly sales for the two weeks before and after, with no promotions in either period. Item A went from $20 to $22, and weekly volume from 1,000 to 920 units. Midpoint change in quantity is -80 ÷ 960 = -8.33 percent. Midpoint change in price is 2 ÷ 21 = 9.52 percent. E = -8.33 ÷ 9.52 = -0.875, so demand is inelastic. Revenue went from $20,000 to $20,240. At a unit cost of $12, gross profit went from $8,000 to $9,200.

Item B went from $50 to $55, and from 400 to 340 units. Quantity change is -60 ÷ 370 = -16.22 percent, price change is 5 ÷ 52.5 = 9.52 percent, and E = -1.70, so demand is elastic. Revenue fell from $20,000 to $18,700. At a unit cost of $30, gross profit still rose, from $8,000 to $8,500. The two items together went from $40,000 to $38,940 in revenue. The average of the two elasticities is about -1.29, which would have called both items elastic and described neither. Two weeks per item is thin, so the next step was a test with matched customer groups.

What you leave with

An elasticity estimate for each item or segment, stated with the price range and period it applies to.
Revenue and profit projections at each candidate price, using unit cost.
A list of confounding factors that were removed, and those that could not be.
A price test design, or a decision to move, with a review date.

Failure points

Estimating from promotions

Price cuts come with displays, advertising, and stock-up buying, so the lift is credited to price alone and elasticity is overstated. Volume often dips after the promotion ends, which the simple before-and-after never shows.

One number for the portfolio

A single average hides items that respond very differently, as in the example. Pricing decisions are made at the item level, so the average justifies the wrong move on both.

Extrapolating beyond the range

An estimate from a five percent cut is applied to a twenty-five percent increase. The demand curve is rarely a straight line over that distance.

Ignoring time and competitors

Short-run elasticity is often lower than long-run, as buyers find substitutes after a while. And a measured number assumes rivals do not respond, which fails exactly when the move is big enough to matter.

Maximizing revenue instead of profit

The revenue rule is applied as if it were the objective. A price increase that lowers revenue can still raise profit, as item B shows, because fewer units also means lower cost. Pricing to protect revenue leaves that profit on the table.

The failures above are usually Commercial Acumen: the work was not tied to money, for the client and/or for you.

Origin

Alfred Marshall defined the elasticity of demand in Principles of Economics (1890). He called demand in a market elastic or inelastic according to whether the quantity bought changes a lot or a little for a given change in price. The measure is a ratio of percentage changes, which makes it independent of units, so it can be compared across currencies, pack sizes, and products.

Two variants matter in practice. Point elasticity uses calculus at a single price. Arc or midpoint elasticity, used below, works from two observed prices and averages them as the base so the answer does not depend on which direction the price moved. Cross-price and income elasticity are close relatives with the same structure. No trademark or license applies.